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97. Ogden RW, Roxburgh DG (1999) A pseudo-elastic model for the Mullins effect in filled
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98. Gent A (1996) A new constitutive relation for rubber. Rubber Chem Technol 69:59–61
99. Kachanov LM (1958) Time of the rupture process under creep conditions. Izvestiya Akad
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100. Ziegler J, Schuster RH (2003) Kautsch Gummi Kunstst 56(4):159–163
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the case of anisotropy. Eur J Mech A Solids 27:28–39
112. Simo J, Taylor R, Pister K (1985) Variational and projection methods for the volume
constraint in finite deformation elasto-plasticity. Comput Meth Appl Mech Eng 51:177–208
113. Eihlers W, Eppers G (1998) The simple tension problem at large volumetric strains computed
from finite hyperelastic material laws. Acta Mech 137:12–27
114. Rivlin R, Saunders D (1952) The free energy of deformation for vulcanized rubber. Trans
Faraday Soc 48:200–206
115. Hartmann S (2001) Numerical studies on the identification of the material parameters of
Rivlin’s hyperelasticity using tension-torsion tests. Acta Mech 148:129–155
116. Pucci E, Saccomandi G (1997) On universal relations in continuum mechanics. Continuum
Mech Thermodyn 9:61–72
117. Johnson AR, Quigley CJ, Freese CE (1995) A viscohyperelastic finite-element model for
rubber. Comput Meth Appl Mech Eng 127:163–180
118. Noll W (1958) A mathematical theory of the mechanical behavior of continuous media. Arch
Rational Mech Anal 2:197–226
119. Wineman A (2009) Nonlinear viscoelastic solids–a review. Math Mech Solids 14:300–366
120. Quintanilla R, Saccomandi G (2007) The importance of the compatibility of nonlinear
constitutive theories with their linear counterparts. J Appl Mech 74:455–460
121. Malkin A (1995) Rheology fundamentals. ChemTec Publishing, Toronto-Scarborough
122. Boltzmann L (1874). Zur Theorie der elastischen Nachwirkung. Sitzungsber Math Naturwiss
Kl Kaiserl Akad Wiss 70:275–306
123. Volterra V (1912) Sur les equations integro-differentielles et leurs applications. Acta Math
35:295–356
268
G. Markovic ´ et al.
96. Horgan CO, Ogden RW, Saccomandi G (2004) A theory of stress softening of elastomers
based on finite chain extensibility. Proc R Soc A 460:1737–1754
97. Ogden RW, Roxburgh DG (1999) A pseudo-elastic model for the Mullins effect in filled
rubber. Proc R Soc A 455:2861–2877
98. Gent A (1996) A new constitutive relation for rubber. Rubber Chem Technol 69:59–61
99. Kachanov LM (1958) Time of the rupture process under creep conditions. Izvestiya Akad
Nauk SSR Otd Tekh Nauk 58:26–31
100. Ziegler J, Schuster RH (2003) Kautsch Gummi Kunstst 56(4):159–163
101. Lion A, Kardelky C (2004) The Payne effect in finite viscoelasticity: constitutive modelling
based on fractional derivatives and intrinsic time scales. Int J Plast 20:1313–1345
102. Beatty M (1996) Nonlinear effects in fluids and solids, chap. 2, Introduction to Nonlinear
Elasticity, 13–112. Plenum Press, New York
103. Holzapfel G (2000) Nonlinear solid mechanics: a continuum approach for engineering.
Wiley, New York
104. Liu IS (2004) On Euclidean objectivity and the principle of material frame-indifference.
Continuum Mech Thermodyn 16:177–183
105. Murdoch AI (2005) On criticism of the nature of objectivity in classical continuum physics.
Continuum Mech Thermodyn 17:135–148
106. Rivlin R (2002) Frame indifference and relative frame indifference. Math Mech Solids
10:145–154
107. Rivlin RS (2005) Some thoughts on frame indifference. Math Mech Solids 11:113–122
108. Truesdell CA, Noll W (1965) The non-linear field theories of mechanics, 3rd edn. Springer,
New York
109. Rivlin R, Ericksen J (1955) Stress-deformation relations for isotropic materials. J Rat Mech
Anal 4:323–425
110. Flory P (1961) Thermodynamic relations for high elastic materials. Trans Faraday Soc
57:829–838
111. Sansour C (2008) On the physical assumptions underlying the volumetric-isochoric split and
the case of anisotropy. Eur J Mech A Solids 27:28–39
112. Simo J, Taylor R, Pister K (1985) Variational and projection methods for the volume
constraint in finite deformation elasto-plasticity. Comput Meth Appl Mech Eng 51:177–208
113. Eihlers W, Eppers G (1998) The simple tension problem at large volumetric strains computed
from finite hyperelastic material laws. Acta Mech 137:12–27
114. Rivlin R, Saunders D (1952) The free energy of deformation for vulcanized rubber. Trans
Faraday Soc 48:200–206
115. Hartmann S (2001) Numerical studies on the identification of the material parameters of
Rivlin’s hyperelasticity using tension-torsion tests. Acta Mech 148:129–155
116. Pucci E, Saccomandi G (1997) On universal relations in continuum mechanics. Continuum
Mech Thermodyn 9:61–72
117. Johnson AR, Quigley CJ, Freese CE (1995) A viscohyperelastic finite-element model for
rubber. Comput Meth Appl Mech Eng 127:163–180
118. Noll W (1958) A mathematical theory of the mechanical behavior of continuous media. Arch
Rational Mech Anal 2:197–226
119. Wineman A (2009) Nonlinear viscoelastic solids–a review. Math Mech Solids 14:300–366
120. Quintanilla R, Saccomandi G (2007) The importance of the compatibility of nonlinear
constitutive theories with their linear counterparts. J Appl Mech 74:455–460
121. Malkin A (1995) Rheology fundamentals. ChemTec Publishing, Toronto-Scarborough
122. Boltzmann L (1874). Zur Theorie der elastischen Nachwirkung. Sitzungsber Math Naturwiss
Kl Kaiserl Akad Wiss 70:275–306
123. Volterra V (1912) Sur les equations integro-differentielles et leurs applications. Acta Math
35:295–356
268
G. Markovic ´ et al.